A382979 a(n) = [(x*y)^n] Product_{k>=1} 1/(1 - x^k + y^k).

1, -2, 4, -20, 78, -282, 1048, -4014, 15456, -59224, 227646, -879694, 3407730, -13219372, 51375286, -200021556, 779870542, -3044448644, 11898709560, -46553635346, 182315752476, -714619687038, 2803342734160, -11005274516610, 43233909672938, -169951684067602, 668474115081988

Offset: 0

Author

Seiichi Manyama, Apr 11 2025

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Main diagonal of A382974.

Cf. A322211, A100221.

Programs

Magma

nmax := 26; prec := 2*nmax + 10; Rx := PowerSeriesRing(Rationals(), prec); Rxy := PowerSeriesRing(Rx, prec); P := Rxy!1; for k in [1..prec] do P *:= 1/(1 - x^k + y^k); end for; seq := [Coefficient(Coefficient(P, n), n) : n in [0..nmax]]; print seq; // Vincenzo Librandi, Apr 12 2025

Mathematica

a[n_]:=SeriesCoefficient[Product[1/(1-x^k+y^k),{k,1,n+5}],{x,0,n},{y,0,n}]; Table[a[n],{n,0,26}] (* Vincenzo Librandi, Apr 12 2025 *)

Formula

a(n) ~ (-1)^n * 4^n / (A100221 * sqrt(Pi*n)). - Vaclav Kotesovec, Apr 13 2025